Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
  • G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
  • G01P5/08—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring variation of an electric variable directly affected by the flow, e.g. by using dynamo-electric effect

Definitions

• the invention relates to a method and an arrangement for the contactless determination of the spatial speed distribution in electrically conductive liquids.
• a preferred area of application of the device is the speed determination in hot and / or chemically aggressive liquid metals and semiconductor melts.
• This disadvantage also relates to the methods for determining the speed in electrically conductive liquids, as specified in USP 5 390 548 and in DE 92 04 374 U1, which are based exclusively on the measurement of electrical potentials at the liquid boundary.
• DE 43 16344 A1 describes a contactless flow measuring device which is based on the fact that an additional magnetic signal is generated in the vicinity of a component generating magnetic fields by turbulence elements of the liquid. By recording this signal at different measuring points and temporally correlating, it is possible to infer runtime differences and thus the liquid velocity between the different measuring points. However, it must be assumed that a given turbulence element flows past two measuring points in succession, which means that the flow structure must be known roughly beforehand. Furthermore, only tangential components of the velocity near the wall can be determined with this method. A spatial Determination of all speed components is not possible with the method specified in DE 43 16 344 AI.
• the invention is based on the object of proposing a method and an arrangement for determining spatial speed distributions in electrically conductive liquids which guarantee reproducible results for all speed components and in which any contact with the liquid or the walls enclosing it is avoided.
• the invention for determining velocity fields v in electrically conductive liquids with the conductivity s is based on the fact that by applying an external magnetic field B 0 (primary field) a current j proportional to the cross product of velocity and primary field, ie
• the measurement of the electrical potential at the edge should be avoided.
• two different primary fields B 0> 1 and B 02 are applied in succession and the respective induced magnetic fields b x and b 2 are measured in the outer area.
• the two primary fields B 0 and B 02 must differ in their direction in the total liquid volume. It is not sufficient if the two primary fields differ only in their amount.
• the magnetic fields b t and b 2 induced under the influence of the primary fields B 0 ⁇ and B 02 are measured at a plurality NB of measuring points outside the liquid.
• the number NB can be selected according to the desired spatial resolution of the speed distribution to be determined.
• the measuring points should enclose the volume of the liquid as evenly as possible. It is sufficient to measure only one magnetic field component at each measuring point. It is recommended that the direction of this magnetic field component is approximately perpendicular to the tangential surface of the liquid at the closest edge point.
• the proportions of the externally applied magnetic fields B 01 k and ( i B 02k at the measuring point k) have to be subtracted from the actual measurement results l and B 2k at the measuring point k must therefore be measured for the flow-free state or otherwise known, for example from calculations ..
• the number of points in the layer closest to the wall should be less than or equal to NB.
• the inverse problem of speed determination is solved from the two data sets of the induced magnetic field in the outer area measured for the two different primary fields. This is done using the least squares method, the mean square deviations of the magnetic fields induced by the assumed speed from the respectively measured values being used as the functionals to be minimized.
• the fact that the speed field is assumed to be free of divergence serves as additional information, which is achieved in the process by installing a corresponding function. To avoid unphysically large amounts of speed when solving the inverse problem, the speed field is regularized by using an additional function.
• An important advantage of the invention is that it is also suitable for determining the speed in hot and / or chemically aggressive liquids, since any contact with the liquid or its boundary is avoided.
• M x and M 2 are matrices of the type (NB, NV) that result from the Biot-Savart law and depend on the respective primary field B 0> 1 and B 02 .
• the boundary of the liquid volume is covered as evenly as possible by a number NU of support points of the electrical potential. While the number NB of the measuring points of the magnetic field and consequently also the number of points NG at which the speed can be determined may be limited to a few tens to about one hundred for measuring reasons, the number NU of the supporting points of the electrical potential can be considerably larger . If u x and u 2 denote the column vectors with NU elements of the electrical potentials (depending on the primary field applied), then the matrix equations apply to them
• u x C u x + N t v, (3a)
• u 2 C u 2 + N 2 v. (3b)
• the regularization method is the so-called Tichonov regularization, in which a functional is added to the functional of the mean quadratic residual deviations for the two measured magnetic fields, which ensures that a suitable norm of the sought speed is minimized -Regularization and the method of the L-curve to be discussed further have been described, for example, in Hansen, P. C, "Analysis of discrete ill-posed problems by means of the L-curve", SIAM Review, Vol. 34, No. 4, pp. 561-580, December 1992.
• the functional of the mean quadratic speed amount and the functional of the mean quadratic curvature of the speed prove to be suitable as the regularization functional.
• the second variant is preferable from a physical point of view, since the velocity field can be assumed to be relatively smooth in many hydrodynamic applications.
• This functional is weighted with an initially still free regularization parameter.
• a function of the mean squared speed divergence is added to ensure freedom from divergence of the speed field sought.
• the system of normal equations for the regularized overall functional is solved for a set of regularization parameters, which is intended to scale the relative weight of the regularization functional in relation to the functionals of the mean quadratic residual deviation over a wide range.
• the forward task for determining the magnetic fields resulting from the respective solution is then solved for each of the regularization parameters.
• the mean square residual deviations from the actual values and the mean square curvature of the speed field are then determined.
• the logarithm of the mean square curvature is then plotted over the logarithm of the weighted mean square residual deviation.
• the resulting curve is typically L-shaped (Tichonov L curve).
• This embodiment includes two pairs of coils 1 and 2, each with a measuring and
• Control unit 3 and 4 for the currents flowing in these coil pairs are connected, one A plurality of magnetic field sensors 5 outside the liquid, which are connected to a signal processor 6 for recording the measured values, an evaluation and storage unit 7 connected downstream of this signal processor and a final output device 8.
• the angle between the coil pairs is selected orthogonally.
• the two coils of the respective coil pairs are traversed by the current in the same direction.
• the diameter and spacing of the coils are chosen so that a relatively uniform penetration of the liquid volume with the generated primary field is ensured.
• the geometry of the coil pairs can expediently be selected on the basis of that of the Helmholtz coils.
• the magnetic Reynolds number Rm sm 0 LV (where m 0 is the permeability of the vacuum) must be less than 1, which, however, is also guaranteed for almost all possible technical and industrial applications. Otherwise, the magnetic fields induced by the speed movement will be of the same order of magnitude as the external magnetic field applied, and the approximations implicitly used for the method according to the invention will fail.
• the pair of coils 2 and the measuring and control unit 4 can be dispensed with if the two primary magnetic fields B 0 ⁇ and B 02 , which differ in their direction, are generated solely by the coil pair 1, which generates an almost constant axial magnetic field with the same polarity of the two coil currents within the cervical area and a so-called cusp field with opposite polarity.
• the coil pair 1 it is advantageous to design the coil pair 1 as a Helmholtz coil pair.

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• Engineering & Computer Science (AREA)
• Aviation & Aerospace Engineering (AREA)
• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Investigating Or Analyzing Materials By The Use Of Magnetic Means (AREA)
• Investigating Or Analyzing Materials By The Use Of Electric Means (AREA)

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• 2000
  • 2000-05-25 DE DE10026052A patent/DE10026052B4/de not_active Expired - Fee Related
• 2001
  • 2001-05-10 DE DE50111805T patent/DE50111805D1/de not_active Expired - Lifetime
  • 2001-05-10 AU AU2001265773A patent/AU2001265773A1/en not_active Abandoned
  • 2001-05-10 AT AT01943043T patent/ATE350671T1/de active
  • 2001-05-10 EP EP01943043A patent/EP1285277B1/fr not_active Expired - Lifetime
  • 2001-05-10 ES ES01943043T patent/ES2278748T3/es not_active Expired - Lifetime
  • 2001-05-10 WO PCT/DE2001/001763 patent/WO2001090762A1/fr active IP Right Grant

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